Well-known principles of induction include monotone induction and different sorts of non-monotone induction such as inflationary induction, induction over well-ordered sets and iterated induction. In this work, we define a logic formalizing induction over well-ordered sets and monotone and iterated induction. Just as the principle of positive induction has been formalized in FO(LFP), and the principle of inflationary induction has been formalized in FO(IFP), this paper formalizes the principle of iterated induction in a new logic for Non-Monotone Inductive Definitions (NMID-logic). The semantics of the logic is strongly influenced by the well-founded semantics of logic programming.